First, this section discusses whether rejection of the null hypothesis should be an all-or-none proposition. Then, it discusses how to interpret non-significant results; for example, it explains why the null hypothesis should not be accepted or should be accepted with caution. It also describes how a non-significant result can increase confidence that the null hypothesis is false.

Interpreting Significant Results


  1. The probability value is the proportion of times that you would get a difference in your sample as large or larger than the one you found if the null hypothesis were actually true. Thus, lower probability values make you more confident that the null hypothesis is false. In this case, the lowest probability value is.003.

  2. The direction of the sample means determines which alternative is adopted. In this example, the sample means show that seniors performed better, so this alternative is accepted.

  3. A significant result lets you conclude the direction of the effect. After a non-significant result, the direction of the difference is uncertain.